Modelling the coverage and annual variation in bilberry yield in Finland

1 SILVA FENNICA Sil a Fennica ol. 50 no. 4 a icle id 1573 Ca ego y: esea ch no e www.sil a ennica. i ISSN-L 0037-5330 | ISSN 2242-4075 (Online) The Finnish Socie y o Fo es Science Na u al Resou ces Ins i u e Finland Ma ju Tu iainen 1, Ja i Miina 2, Kauko Salo 3 and Juha-Pekka Ho anen 2 Modelling he co e age and annual a ia ion in bilbe y yield in Finland Tu iainen M., Miina J., Salo K., Ho anen J.-P. (2016). Modelling he co e age and annual a i- a ion in bilbe y yield in Finland. Sil a Fennica ol. 50 no. 4 a icle id 1573. 12 p. h p://dx.doi. o g/10.14214/s .1573. Highligh s • The highes bilbe y co e age was ound in mesic hea h o es s and ell o es s. • On pea lands he co e age was, on a e age, lowe han on mine al soil si es. • The app oach in oduced in his s udy o calcula ing annual be y yield indices is a p omising way o es ima ing o al annual bilbe y yields o e a gi en pe iod o ime. Abs ac The co e age o bilbe y (Vaccinium my illus L.) was modelled as a unc ion o si e and s and cha ac e is ics using he pe manen sample plo s o he Na ional Fo es In en o y (NFI) (Model 1). The sample si es consis ed o mine al soil o es s as well as ells and pea land si es. Annual a ia- ion in he bilbe y yield (Model 2) was analysed based on measu emen s o e 2001–2014 in he pe manen sample plo s (so-called MASI plo s) in a ious a eas o Finland. We de i ed annual bilbe y yield indices om he yea e ec s o Model 2 and in es iga ed whe he hese indices could be used o es ima e annual a ia ion in bilbe y c ops in Finland. The highes bilbe y co e age was ound in mesic hea h o es s and ell o es s. On pea lands he co e age was, on a e age, lowe han on mine al soil si es; he pea land si es wi h mos bilbe y co e age we e meso-oligo ophic and oligo ophic sp uce mi es and oligo ophic pine mi es. Ou bilbe y yield indices showed simila a ia ion o hose de i ed om he mean annual be y yields epo ed and calcula ed ea lie using he MASI plo s; he co ela ion be ween he indices was 0.795. This app oach o calcula ing annual be y yield indices is a p omising way o es ima ing o al annual bilbe y yields o e a gi en pe iod o ime. Models 1 and 2 can be used in conjunc ion wi h he Miina e al.’s (2009) bilbe y yield model when bilbe y co e age, a e age annual yield and annual a ia ion in he yield a e o be p edic ed in o es planning. Keywo ds abundance; be y yield; gene alised linea mixed model; Vaccinium my illus L. Add esses 1 Uni e si y o Eas e n Finland, School o Fo es Sciences, P.O. Box 111, FI-80101 Joensuu, Finland; 2 Na u al Resou ces Ins i u e Finland (Luke), Managemen and P oduc ion o Renewable Resou ces, Box 68, FI-80101 Joensuu, Finland; 3 Na u al Resou ces Ins i u e Finland (Luke), Bio-based Business and Indus y, Box 68, FI-80101 Joensuu, Finland E-mail[email p o ec ed] Recei ed 25 Feb ua y 2016 Re ised 31 Augus 2016 Accep ed 1 Sep embe 2016 2 Sil a Fennica ol. 50 no. 4 a icle id 1573 · Tu iainen e al. · Modelling he co e age and annual a ia ion in… 1 In oduc ion Bilbe y (Vaccinium my illus L.) is one o he mos abundan wild be y species in Finland (Sale- maa 2000). I has adap ed o a wide ange o di e en si e and land ypes in coni e ous ecosys ems and, as a esul , is widely dis ibu ed ac oss di e en pa s o Eu ope and no he n Asia (Ri chie 1956; Coudun and Gégou 2007). In No h Ame ica, he e a e se e al species closely ela ed o V. my illus (Ri chie 1956). In Finland, bilbe y is ypical and abundan especially in coni e hea h o es s o medium e ili y (Laakso e al. 1990; Salemaa 2000). I is also p esen and p oducing c ops in many ma ginal o es ypes (e.g. ell o es s), and on p is ine and d ained pea land si es (Sa as o 1961; Salemaa 2000). I has been es ima ed ha Finnish o es s and pea lands could p oduce an a e age o abou 184 million kg o bilbe ies annually (Tu iainen e al. 2005, 2007), howe e wild be y yields a y g ea ly om yea o yea due o e.g. os , pollina ion success and a ia ion in p ecipi a ion and empe a u e (Raa ikainen 1993; Wallenius 1999). Tu iainen e al. (2011) calib a ed he o al bilbe y yield in an a e age c op yea o di e en c op yea s using he in en o y da a on wild be ies ( e e ed o as MASI da a; Salo 1999) which was collec ed om pe manen be y sample plo s in 1997–2008. The calib a ion was a wo-s age p ocess. Fi s , mean annual na ional bilbe y yields (kg ha–1) we e calcula ed om he numbe s o bilbe ies coun edannuallyon heMASIsampleplo sandsi e-speci ic igu es o  he eshweigh o abilbe y. The a i hme ical mean be y yield was calcula ed on he basis o mean annual be y yields. Second, he minimum and maximum alues om he se ies o mean annual be y yields o he s udy pe iod (1997–2008) we e di ided by he a i hme ical mean be y yield and mul iplied by 184 million kg (i.e. o al be y yield du ing an a e age c op yea ). Tu iainen e al. (2011) hus calcula ed ha o al annual bilbe y yields in Finland would a y be ween app oxima ely 90 and 310 million kg. Picking wild be ies is an impo an o es cus om in he no he n hemisphe e, pa icula ly in he No dic coun ies and o me e i o ies o he USSR (Lee e al. 2007; Tu iainen and Nuu inen 2012). I is also so ha oday bo h he public and p i a e o es landowne s place a high alue on he mul iple-use aspec s o o es s and objec i es o he han wood p oduc ion ha e go inc easing weigh in o es y decision-making (Kangas 1998; Rämö e al. 2013; Filyushkina e al. 2016). Consequen ly, p oduc ion unc ions a e needed o non-wood o es p oduc s and se ices so ha he a ious aspec s o o es use – bo h imbe and non- imbe – can be in eg a ed in o o es plan- ning calcula ions (Bo ges e al. 2014). In hese unc ions, si e ype and s and cha ac e is ics a e he mos easonable p edic o s as hey a e known in o es planning sys ems. A numbe o models o he species Vaccinium ha e been de eloped in di e en coun ies. Fo example, Coudun and Gégou (2007) used clima ic and edaphic ac o s o help p edic ing he abundance o bilbe y in F ench’s o es s. In Canada, models o lowbush bluebe ies (Hall e al. 1982) and Vaccinium i is-idaea L. (K ebs e al. 2009) we e de eloped o p edic he yield using clima ic a iables. In Sweden, a ious ecosys em se ices (including bilbe y p oduc ion) we e modelled using bo h s and cha ac e is ics and clima ic and edaphic ac o s as p edic o s (Gam- eld e al. 2013). Howe e , none o he models men ioned abo e a e sui able o o es planning calcula ions because o he p edic o s hey employ. In Finland, se e al models o he yields o bilbe y and cowbe y (V. i is-idaea L.) ha e been de eloped (Ihalainen and Pukkala 2001; Ihalainen e al. 2002, 2003, 2005; Miina e al. 2009; Tu iainen e al. 2013). All hese models ha e been p epa ed o o es planning pu poses. So a only Miina e al. (2009) ha e aken in o accoun he annual a ia ion in bilbe y yields using he MASI sample plo measu emen s om 2001–2007. The models o Miina e al. (2009) p edic ed bilbe y co e age as a unc ion o si e e ili y and s and cha ac e is ics, and used hese esul s o p edic be y yield and annual a ia ion in be y yield as a unc ion o bilbe y co e age and s and 3 Sil a Fennica ol. 50 no. 4 a icle id 1573 · Tu iainen e al. · Modelling he co e age and annual a ia ion in… cha ac e is ics. The co e age model can be applied o mine al soil si es h oughou he coun y bu he yield model is based on egional da a om No h Ka elia, Finland. In his s udy, he wo k o Miina e al. (2009) was con inued so ha he model o he co e - age o bilbe y conside s no only mine al soil si es bu also pea land si es and ells (Model 1). Fu he , he annual a ia ion in bilbe y yield du ing 2001–2014 (Model 2) was modelled using a conside ably longe ime se ies o da a om he MASI sample plo s han in he ea lie s udy by Miina e al. (2009). Finally, we in es iga ed whe he he annual yield indices de i ed om Model 2 could be used o es ima e o al annual bilbe y c ops in Finland o he 2001–2014 pe iod. 2 Ma e ials and me hods 2.1 Ma e ials Da a we e collec ed o he pe cen age co e age o bilbe y on he pe manen sample plo s (300 m2) o he Finnish Na ional Fo es In en o y (NFI) in 1995 (so-called PSP3000 da a) (Finnish Fo es Resea ch Ins i u e 1995). Miina e al. (2009) and Tu iainen e al. (2013) used he same da a in hei s udies and ha e desc ibed he in en o y me hod in de ail. Sample plo s ep esen ing se en di e en ca ego ies (a–g) we e used in his s udy. The ca ego ies we e ini ially de eloped o model- ling he co e age o cowbe y and we e selec ed on he basis ha cowbe y occu s equen ly and abundan ly on all o hem (Tu iainen e al. 2013). As bilbe y and cowbe y e y o en g ow side by side, a he same si es, i seemed easonable o use he same ca ego ies in his s udy. Ca ego ies (a–e) pe ained o o es land and we e as ollows: a) mine al soils, b) sp uce mi es – ans o ming phase, c) sp uce mi es – ans o med phase, d) pine mi es – ans o ming phase, and e) pine mi es – ans o med phase. In he case o poo ly p oduc i e land and unp oduc- i e (was e) land, only ell o es s ( ) and summi s (g) (i.e. si e quali y class VIII; Finnish Fo es Resea ch Ins i u e 1995; Tomppo e al. 2011) we e conside ed in he modelling (Supplemen a y ile1,a ailablea h p://dx.doi.o g/10.14214/s .1573).I iswo hno ing ha when alkingb ie ly abou ells, bo h ell o es s and summi s a e mean . A o al o 2515 sample plo s om he PSP3000 da a we e included in he da ase o his s udy. Fo all sample plo s bilbe y co e age was es ima ed om ou 2 m2 quad a es; he a e ages we e used as he sample plo -wise (s and-wise) es ima es o abundance. Due o he he e ogenei y o he sample plo , 11% o he plo s we e di ided in o wo o h ee s ands. As a esul , 2801 s ands we eincludedin heanalyses(Suppl. ile1).Thes andcha ac e is icsandmeanbilbe yco e age we e calcula ed o all s ands and used in he modelling. A desc ip ion o s and cha ac e is ics by ca ego ies is gi en by Tu iainen e al. (2013, p. 6). The da a had a hie a chical s uc u e because he sample plo s we e loca ed in 983 clus e s, which in u n we e loca ed in 367 municipali ies and 14 o es y cen e egions. The annual a ia ion in bilbe y yield was analysed using MASI da a o he 2001–2014 pe iod (Salo1999).TheMASIin en o y epo sannualcoun so  ipebilbe ieson i epe manen 1m2 quad a es loca ed in o es s ands which had been ound o be good g owing si es o he species. The mean annual numbe o ipe bilbe ies and he mean bilbe y co e age o hese quad a es we e used in modelling. The da ase included 306 obse a ions o mean annual bilbe y numbe s in 50 s ands (Supplemen a y ile2,a ailablea h p://dx.doi.o g/10.14214/s .1573). S ands we e cha ac e ised in e ms o si e ype, dominan ee species, s and age and basal a ea. The majo i y (60%) o s ands in he da ase we e domina ed by pine (Pinus syl es is L.), 32% we e domina ed by sp uce (Picea abies (L.) Ka s .) and he es by deciduous ee species, mainly bi ches (Be ula pendula Ro h, B. pubescens Eh h.). The s ands we e loca ed in 29 municipali ies and in 13 o es y cen e egions. 4 Sil a Fennica ol. 50 no. 4 a icle id 1573 · Tu iainen e al. · Modelling he co e age and annual a ia ion in… 2.2 S a is ical modelling Models we e p epa ed o he mean pe cen age bilbe y co e age (Model 1) and he mean numbe o bilbe ies in he s and (Model 2) using gene alised linea mixed models (GLMMs) (Supplemen a y ile3,a ailablea h p://dx.doi.o g/10.14214/s .1573). Model 1 was exp essed using a logi -link unc ion wi h a binomial esponse, and Model 2 using a log-link unc ion wi h a Poisson esponse. In Model 1 all he con inuous p edic o s (e.g. s and age and basal a ea) and ca ego ical p edic o s (e.g. si e quali y classes in di e en ca ego ies a–e) had o be logical and s a is ically signi ican a  he0.05le el,wi hnosys ema ice o sin esiduals.Theco e agewasmodelled and he ca ego ies we e combined as desc ibed by Tu iainen e al. (2013) and hence ca ego ies (b) and (c) we e combined and a e la e join ly desc ibed as ‘sp uce mi es’; simila ly ca ego ies (d) and (e) we e combined and a e join ly desc ibed as ‘pine mi es’. In Model 2, bilbe y co e age, al i ude and mean e ec i e empe a u e sum we e used as po en ial ixedp edic o s.Theyea e ec sin2001–2014we econside edusingindica o  a iables as ixedp edic o s. We adjus ed o he mul i-le el hie a chy and unbalanced s uc u e o he da ase s by includ- ing andom e ec s a di e en le els. We adjus ed o o e -dispe sion in he esponse a iables by adding an addi ional andom e m a he bo om le el (‘pseudo’ le el). The GLMMs we e es ima ed using he glmmPQL unc ion o he R so wa e (R De elopmen Co e Team 2012). 2.3 Simula ions The pe o mance o Model 1 was illus a ed by p edic ing he bilbe y co e age in a ious s ands whose ini ial cha ac e is ics, de elopmen and managemen we e simula ed using he Mo i s and simula o (Hynynen e al. 2005). The simula ed s ands we e loca ed in sou he n Finland, wi h he empe a u e sum and al i ude se a 1200 dd. and 100 m, espec i ely. We used he same pine and sp uce s ands ep esen ing se e al si e ypes on mine al soils as Miina e al. (2009), and he same pine s ands on pine mi es as Tu iainen e al. (2013). We also simula ed sp uce s ands on sp uce mi es (si es II and III) using he Mo i simula o . 2.4 Be y yield indices Bilbe y yield indices we e calcula ed om he yea e ec s in Model 2. The yea e ec s we e ans o med in o exponen ial o m, mul iplied by one hund ed and scaled o ha e a mean o 100. The indices ob ained in his s udy we e compa ed wi h be y yield indices de i ed om he mean annual be y yields p esen ed by Salo (2015). Salo (2015) calcula ed a se ies o mean annual bilbe y yields o 1997–2013 using MASI da a and he me hod desc ibed by Tu iainen e al. (2011). Fo he pu pose o compa ison we also scaled Salo’s (2015) mean annual be y yields o ha e a mean o 100. 3 Resul s 3.1 Model o bilbe y co e age In he case o mine al soils, Model 1 o bilbe y co e age p oduced esul s e y simila o hose desc ibed by Miina e al. (2009); he highes co e age was ound on mesic hea h o es s (si e III, Table 1). On sub-xe ic hea h o es s (si e IV) and he b- ich hea h o es s (si e II), he co e age 5 Sil a Fennica ol. 50 no. 4 a icle id 1573 · Tu iainen e al. · Modelling he co e age and annual a ia ion in… was 63% and 57% o ha on si e III espec i ely. On ocky and sandy soils (VII) and xe ic hea h o es s (V) he co e age was conside ably lowe , and on he b- ich o es s (I), i was sca ce. On mine al soils bilbe y co e age inc eased wi h s and age and s and basal a ea up o he age o 175 yea s and a densi y o 26 m2 ha–1, a e which co e age g adually dec eased. I is wo h no ing ha s andbasala eawasasigni ican p edic o no onlyonmine alsoilsbu alsoonsp uce Table 1. The mul i-le el binomial model (Model 1) es ima ed o he mean pe cen age co e age o bilbe y on he 2 m2 quad a es in he s ands o he PSP3000 da a. Si es I–V and VII–VIII e e o di e en si e quali y classes (see Suppl. ile1).Mine alsoils,sp ucemi esandpinemi espe ain o o es land,i.e.ca ego ies(a–e)o  hiss udy. Va iable Es ima e S d e o - alue Odds a io p- alue In e cep –4.3356 0.0934 –46.44 0.013 < 0.001 Si e ( e . III, mine al soils) a si e I, mine al soils –2.4140 0.1708 –14.14 0.089 < 0.001 si e II, mine al soils –0.5627 0.0630 –8.93 0.570 < 0.001 si e IV, mine al soils –0.4702 0.0513 –9.17 0.625 < 0.001 si e V, mine al soils –1.6286 0.1085 –15.01 0.196 < 0.001 si e VII, mine al soils –1.3500 0.2149 –6.28 0.259 < 0.001 si es≤II,sp ucemi es –1.1044 0.1173 –9.41 0.331 < 0.001 si es≤III,pinemi es –0.4081 0.1220 –3.35 0.665 0.001 si e IV, pine mi es –0.2592 0.0812 –3.19 0.772 0.002 si e V, pine mi es –1.0210 0.0922 –11.08 0.360 < 0.001 si e VIII, poo ly p oduc i e land 1.1348 0.1893 6.00 3.111 < 0.001 A i icialRegenb, mine al soils –0.2713 0.0500 –5.42 0.762 < 0.001 Fo me Ag Land c, mine al soils –1.7342 0.1468 –11.81 0.177 < 0.001 Sp uce d, mine al soils –0.1196 0.0522 –2.29 0.887 0.023 Deciduous ees d on si es I and II, mine al soils –0.7146 0.1123 –6.37 0.489 < 0.001 Deciduous ees d, sp uce mi es –0.7355 0.1246 –5.90 0.479 < 0.001 Al i ude (m) 0.0040 0.0005 8.06 1.004 < 0.001 Al i ude2/100 (m), poo ly p oduc i e and was e land –0.0004 0.0001 –3.97 0.999 < 0.001 S and age (a), mine al soils 0.0094 0.0011 8.43 1.009 < 0.001 S and age2/100 (a), mine al soils –0.0027 0.0005 –5.32 0.997 < 0.001 S and basal a ea (m2 ha–1), o es land e0.1071 0.0055 19.35 1.113 < 0.001 S and basal a ea2/100 (m2 ha–1), o es land e–0.2050 0.0151 –13.59 0.815 < 0.001 Va iance componen s a o es y cen e egion le el 0.0187 (14) municipali y le el 0.1279 (367) clus e le el 0.1328 (983) sample plo le el 0.1585 (2515) s and le el (‘pseudo’ le el) 0.4913 (2801) a The pa ame e es ima es o si e a iables “si e III, sp uce mi es”, “si e IV, sp uce mi es” and “si e VIII, was e land” we e no s a is i- callysigni ican . bA i icialRegen(a i icial egene a ion)isanindica o  a iable o  he egene a ionme hod( e .na u al egene a ion). c Fo me Ag Land ( o me ag icul u al land) is an indica o a iable o s and his o y ( e . o me o es ). d An indica o a iable o he dominan ee species ( he e e ence is o he ee species). e In his con ex , o es land e e s o ca ego ies (a–e) o his s udy. The numbe o obse a ions a each le el is gi en in pa en heses. A andom e m a ‘pseudo’ le el accoun s o he o e dispe sion. 6 Sil a Fennica ol. 50 no. 4 a icle id 1573 · Tu iainen e al. · Modelling he co e age and annual a ia ion in… Fig. 1. P edic edco e ageo bilbe yinpineandsp uces andso di e en si e e ili ies(i.e.si esI–V;see hede ini ionsinSuppl. ile1).Thede elopmen o s ands, ep esen ing mine al soils (A, B), pine mi es (C) and sp uce mi es (D) in sou he n Finland, was simula ed using he Mo i simula o (a ows indica e hinnings). 7 Sil a Fennica ol. 50 no. 4 a icle id 1573 · Tu iainen e al. · Modelling he co e age and annual a ia ion in… andpinemi es.Onmine alsoilsandsp ucemi es, hedominan  eespecieswasalsoasigni ican  p edic o o bilbe y abundance. The co e age was lowe in sp uce-domina ed mine al soil o es s han pine-domina ed o es s. The nega i e e ec o deciduous ees on bilbe y co e age applied on mine al soils (si es I and II) and sp uce mi es. Meso-oligo ophic(III)andoligo ophicsp ucemi es(IV)didno di e signi ican ly om mesic hea h o es s wi h espec o bilbe y abundance (Table 1). Co e age a he o he si es (I–II) on sp uce mi es was, on a e age, one hi d o he co e age on si e III, which is on mine al soils ( he e e ence in Model 1). O he pine mi e si es, si e IV had he highes bilbe y co e age, al hough no as high as si e III (on mine al soils) and si es III and IV (on sp uce mi es). A he si es on meso-oligo ophic and mo e e ile pine mi es (I–III), he co e age was wo hi ds o ha on si e III (mine al soils), whils on poo oligo-omb o ophic pine mi es (V), i emained conside ably lowe . Model 1 indica ed ha co e age on poo ly p oduc i e land, i.e. on ell o es s a high al i ude, was highe han on si e III, on mine al soils (Table 1). In addi ion al i ude had a posi i e e ec on bilbe y co e age in all ca ego ies (a–g), sugges ing ha co e age is, on a e age, highe in eas e n and no he n Finland han in wes e n and sou he n Finland. Howe e , bo h al i ude and s and age and basal a ea a e ac o s in he la gescale a ia ion in bilbe y co e age in Model 1. In he simula ed s ands he e ec o si e e ili y on p edic ed co e age was clea and he co e age inc eased wi h s and age and basal a ea (Fig. 1). In mos cases co e age was empo a - ilya ec edby hinnings,bu alwaysdec easedsigni ican ly ollowing egene a ion elling.On a e age, co e age was highe on mine al soils han on pine and sp uce mi es. 3.2 Annual a ia ion in bilbe y yields Du ing he s udy pe iod o 2001–2014, p edic ed yea e ec in Model 2 o he numbe o bilbe ies was highes in 2005 and 2012, and lowes in 2002 and 2010 (Fig. 2, Table 2). The sample mean and a iance o  he ixedyea e ec so Model2we e0.1374and0.0367 espec i ely. Fig. 2. Bilbe y yield indices calcula ed on he basis o Model 2 (Table 2) and mean annual bilbe y yields (kg ha–1) p esen ed by Salo (2015). The o me index se ies co e s yea s 2001–2014 and he la e one yea s 1997–2013. In bo h se ies, he mean alue o he indices is 100. 8 Sil a Fennica ol. 50 no. 4 a icle id 1573 · Tu iainen e al. · Modelling he co e age and annual a ia ion in… The bilbe y yield indices in his s udy show simila a ia ion o hose de i ed om Salo’s (2015) s udy; he co ela ion be ween he indices in he wo s udies was 0.795. Acco ding o Salo (2015), he bes and wo s bilbe y c ops we e ob ained in 2012 and 2004 espec i ely. Fo he 2001–2013 pe iod he e is ag eemen be ween he index se ies on he abo e- and below-a e age yea s, wi h he excep ion o 2009. Howe e , he ange o he indices calcula ed in his s udy was smalle han ha in Salo’s (2015) s udy (69–150 and 50–180 espec i ely). 4 Discussion This s udy ep esen s a con inua ion o wo k by Miina e al. (2009) and Tu iainen e al. (2011). Ou model o bilbe y co e age (Model 1) conside ed a wide ange o si es, including o he si es whe ebilbe yoccu sin he ieldlaye (ca ego iesb–g)aswellas hemine alsoil o es s(ca - ego y a) conside ed by Miina e al. (2009). Co e ing a wide ange o si es was needed, because one hi d o o es y land in Finland is g owing on pea lands (Na u al Resou ces Ins i u e Finland (Luke) 2015) which a e no conside ed by he ea lie model o Miina e al. (2009). Model 1 was p epa ed o o es planning pu poses and i can be used oge he wi h he yield model o Miina e al. (2009: Table 3). Table 2. Themul i-le elPoissonmodel(Model2)es ima ed o  hemeannumbe o bilbe ieson i e1m2 quad a es in MASI s ands, measu ed in 2001–2014. Va iable Es ima e S d e o - alue p- alue In e cep 4.4549 0.7005 6.36 <0.001 Yea e ec ( e . 2006) 2001 0.1960 0.1719 1.14 0.256 2002 –0.2007 0.1806 –1.11 0.268 2003 0.4469 0.1708 2.62 0.009 2004 –0.0602 0.1681 –0.36 0.721 2005 0.5694 0.1622 3.51 0.001 2007 0.3161 0.1708 1.85 0.066 2008 0.0533 0.1647 0.32 0.747 2009 0.0960 0.1598 0.60 0.549 2010 –0.2072 0.1612 –1.29 0.200 2011 0.2025 0.1569 1.29 0.198 2012 0.5280 0.1632 3.24 0.001 2013 –0.0334 0.1723 –0.19 0.846 2014 0.0164 0.1788 0.09 0.927 Co e age o bilbe y, % 0.0135 0.0057 2.38 0.028 1000/Tempe a u e sum (dd) –1.0888 0.5101 –2.13 0.050 Va iance componen s a a o es y cen e egion le el <0.0001 (13) municipali y le el 0.1235 (29) s and le el 0.1132 (50) s and × yea le el (‘pseudo’ le el) 0.2656 (306) a The numbe o obse a ions a each le el is gi en in pa en heses. A andom e m a ‘pseudo’ le el accoun s o he o e dispe sion. 9 Sil a Fennica ol. 50 no. 4 a icle id 1573 · Tu iainen e al. · Modelling he co e age and annual a ia ion in… In he case o mine al soil o es s (ca ego y a), ou esul s on bilbe y co e age we e e y simila o hose o Miina e al. (2009). Miina e al. (2009) conside ed hei esul s in he con ex o ea lie empi ical indingsandconcluded ha  heywe econsis en wi h hese indings(seealso Gam eld e al. 2013; Hedwall e al. 2013). I ollows ha ou esul s a e also consis en wi h he empi ical indings. Bilbe y co e age on pea lands was, on a e age, lowe han on mine al soil si es (Salemaa 2000). O he pea land si es, si es III and IV on sp uce mi es and si e IV on pine mi es had he highes bilbe yco e age.These indingsa einlinewi hea lie s udies(Sa as o1961;Salemaa 2000). Acco ding o Model 1, deciduous ees dec eased bilbe y co e age on bo h sp uce mi es and hemos  e ilemine alsoilsi es.To hebes o ou knowledge hisis he i s s udy oconside  he e ec s o ee species on bilbe y co e age on pea lands. Bilbe y was highly abundan on ell o es s, and al i ude also had a posi i e e ec on bil- be y co e age. In no he n Finland bilbe y g ows on poo e si es han in sou he n Finland owing o he highe ela i e humidi y and highe soil mois u e in he no h. Bilbe y is widesp ead on he lowe slopes o ells and moun ains, bu i does no occu a such high al i udes as Vaccinium i is-idaea L. o Empe um nig um L. (Salemaa 2000). Ou modelling o bilbe y co e age was based on an ex ensi e da ase collec ed om he pe manen sampleplo so  heFinnishNFIin1995(Suppl. ile1).TheMASIda ase wascon- side ablysmalle (Suppl. ile2)andcomp isedmainlyda a omma u es andso mediumsi e e ili ywhichhadbeen ound obegood o bilbe y.The e o e,i wasun easible o i anew yield model in his s udy, and, al hough i is based on egionally limi ed da a, we ecommend he bilbe y yield model o Miina e al. (2009) o u u e use (Kilpeläinen e al. 2016). We used he MASI da a om 2001–2014 o model annual a ia ion in bilbe y yields (Model 2). Ou Model 2 is based on da a om wice as many yea s as he model by Miina e al. (2009) and we he e o e ecommend ha i is used in conjunc ion wi h he Miina e al.’s (2009) bilbe y yield model when bo h a e age annual yield and annual a ia ion in he yield a e o be p edic ed. In hiss udy,we i s de i edannualbilbe yyieldindices om heyea e ec so Model2 and hen in es iga ed whe he hese indices could be used o es ima e annual a ia ion in bilbe y c ops in Finland. The bilbe y yield indices a ied qui e simila ly wi h hose o Salo (2015) (Fig. 2). The e a e se e al possible easons o he di e ences be ween hese wo index se ies. Fi s ly, we used, on a e age, ewe MASI s ands pe yea han Salo (2015) (22 s. 69 s ands pe yea ). We used only hose MASI s ands o which da a on s and cha ac e is ics and bilbe y co e age we e a ail- able in addi ion o da a on bilbe y numbe s and si e e ili y. Secondly, by using a mixed modelling app oach we we e able o adjus o he unbalanced, c oss-co ela ed s uc u e o he MASI da a. Da a we e no a ailable o all sample plo s o e e y yea and obse a ions om a gi en yea we e c oss-co ela ed due o annual a ia ion in condi ions. Thi dly, Tu iainen e al. (2011) and Salo (2015) calcula ed mean annual bilbe y yields (kg ha–1) using he me hod desc ibed by Tu iainen e al. (2011), which used a e age weigh s o ipe bilbe ies on di e en si e e ili ies. The weigh s we e ob ained om ea lie s udies by Kuchko (1988) and Ihalainen e al. (2003). Howe e , one can ques ion whe he he weigh s used we e accu a e enough (c . E onen 2004). I should also be no ed ha Tu iainen e al. (2011) did no conside annual a ia ion in bilbe y weigh . In his s udy we de i ed bilbe y yield indices di ec ly om he numbe o bilbe ies wi hou con e ing be y coun s in o esh weigh s. In conclusion, he modelling app oach in oduced in his s udy is a p omising way o es ima ing o al annual bilbe y yields o e a gi en pe iod o ime. The app oach can also be applied o cowbe y. Howe e , models o annual a ia ion in be y yield should be based on mo e comp ehensi e da a han we e used in his s udy. Access o a comp ehensi e da ase is equi ed o de e mine how o adjus be y yields o an a e age c op yea o p edic o al yield in a gi en